If a complex matrix of order 3 satisfies a polynomial of degree 3 is the polynomial characteristic polynomial for all such matrix?
If a matrix of order n satisfies a monic polynomial of degree n in a algebraically closed field is the polynomial characteristic polynomial?
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linear-algebra
1 Answers
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The matrix with every entry zero, $O$, satisfies $X(X+1)(X+2)$ but its characteristic polynomial is $X^3$.